Existence of infinitely many solutions for the one-dimensional Perona-Malik model

被引：46

作者：

Zhang, KW ^{[1
]}

机构：

[1] Univ Sussex, Dept Math, Brighton BN1 9RF, E Sussex, England

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2006年 / 26卷 / 02期

关键词：

Perona-Malik model; one-dimensional; infinitely many solutions; differential inclusion; relaxation property;

D O I：

10.1007/s00526-005-0363-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the existence of infinitely many weak solutions for the the one-dimensional version of the well-known and widely used Perona-Malik anisotropic diffusion equation model in image processing. We establish the existence result under the homogeneous Neumann condition with smooth non-constant initial values. Our method is to convert the problem into a partial differential inclusion problem.

引用

页码：171 / 199

页数：29

共 50 条

[1] Existence of infinitely many solutions for the one-dimensional Perona-Malik model
Kewei Zhang
Calculus of Variations and Partial Differential Equations, 2006, 26 : 171 - 199
[2] Entire solutions of the one-dimensional Perona-Malik equation
Gobbino, Massimo
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (05) : 719 - 743
[3] A CLASS OF LOCAL CLASSICAL SOLUTIONS FOR THE ONE-DIMENSIONAL PERONA-MALIK EQUATION
Ghisi, Marina
Gobbino, Massimo
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 361 (12) : 6429 - 6446
[4] Young measure solutions and instability of the one-dimensional Perona-Malik equation
Taheri, S
Tang, Q
Zhang, KW
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 308 (02) : 467 - 490
[5] CONVEX INTEGRATION AND INFINITELY MANY WEAK SOLUTIONS TO THE PERONA-MALIK EQUATION IN ALL DIMENSIONS
Kim, Seonghak
Yan, Baisheng
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2015, 47 (04) : 2770 - 2794
[6] Staircasing effect for minimizers of the one-dimensional discrete Perona-Malik functional
Picenni, Nicola
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2024, 30
[7] On the convexification of the Perona-Malik diffusion model
Maiseli, Baraka Jacob
SIGNAL IMAGE AND VIDEO PROCESSING, 2020, 14 (06) : 1283 - 1291
[8] Ramp preserving Perona-Malik model
Chen, Qiang
Montesinos, Philippe
Sen Sun, Quan
Xia, De Shen
SIGNAL PROCESSING, 2010, 90 (06) : 1963 - 1975
[9] An Extended Perona-Malik Model Based on Probabilistic Models
Mescheder, L. M.
Lorenz, D. A.
JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2018, 60 (01) : 128 - 144
[10] Radial weak solutions for the Perona-Malik equation as a differential inclusion
Kim, Seonghak
Yan, Baisheng
JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 258 (06) : 1889 - 1932

← 1 2 3 4 5 →